# Algebra II : Number Sets

## Example Questions

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### Example Question #1 : Number Sets

If , , and , then find the following set:

Explanation:

The union is the set that contains all the numbers from  and .  Therefore the union is

### Example Question #2 : Number Sets

If , , and , find the following set:

Explanation:

The intersection is the set that contains only the numbers found in all three sets. Therefore the intersection is .

### Example Question #3 : Number Sets

If , , and , find the following set:

Explanation:

The intersection is the set that contains the numbers that appear in both  and .  Therefore the intersection is .

### Example Question #1 : Number Sets

If , , and , find the following set:

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .

### Example Question #5 : Number Sets

If , , and , find the following set:

Explanation:

The union is the set that contains all of the numbers found in all three sets.  Therefore the union is .  You do not need to re-write the numbers that appear more than once.

### Example Question #6 : Number Sets

If , , and , find the following set:

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .

### Example Question #1 : Number Sets

Which set of numbers represents the union of E and F?

Explanation:

The union is the set of numbers that lie in set E or in set F.

.

In this problem set E contains terms , and set F contains terms . Therefore, the union of these two sets is .

### Example Question #1 : Number Sets

Express the following in Set Builder Notation:

Explanation:

and stands for OR in Set Builder Notation

### Example Question #9 : Number Sets

Find the intersection of the two sets:

Explanation:

To find the intersection of the two sets, , we must find the elements that are shared by both sets:

### Example Question #2 : Number Sets

What type of numbers are contained in the set ?

Natural

Complex

Irrational

Imaginary

Integers

Integers

Explanation:

We can use process of elimination to find the correct answer.

It can't be Imaginary because we're not dividing by a negative number.

It can't be Complex because the number's aren't a mix of real and imaginary numbers.

It can't be Irrational because they aren't fractions.

It can't be Natural because there are negative numbers.

It must be Integers then!  All the numbers are whole numbers that fit on the number line.

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